Usually, it is "emissions". I would only use "production" if the carbon dioxide was a product that was intended to be made. "Output" would be acceptable as a side-effect as with "emissions".
Can't decide whether we can use the singular and plural of carbon-dioxide emissions.
Can we also talk about carbon-dioxide production or output as a synonym?
You can talk about the carbon dioxide emission of a certain factory, or as a global problem. I think that singular 'emission' is suitable in most cases - as is 'emissions'.
No, it can't be a synonym for production, since you can produce CO2 without emitting it.